Although perhaps similar at first glance to the other two regimes, the subexponential regime is more sophisticated and requires a much finer analysis. In the subexponential regime, \(a_T\ll T\) , we prove that the SVP formulation of [1]} with cost
\(\hat{c}(x,\hat{\mathbb {P}}_T,T)=c (x,\hat{\mathbb {P}}_T)+\sqrt{\frac{2a_T}{T}\mathrm {Var}_{\hat{\mathbb {P}}_T}(\ell (x, \xi ))},\quad \forall x \in \mathcal {X},\; \forall T \in \mathbf {N},\) 
